Finite Group Databasebeta

← #14640372

Subgroups — #14640372

Order 2816.

284 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 91 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13068469C211yesmaximal, characteristic
2#13068365C211yesmaximal, characteristic
3C11×#1839C211yesmaximal, characteristic
4C43×C11C2211yescharacteristic
5C2×C4⋊(C11⋊C8)—21no—
6C2×#66867—21no—
7C2×#66867C412yes—
8C11×#336—21no—
9C11×#336—21no—
10C11×#336C412yes—
11#10622162—21no—
12#10622162—21no—
13#10622162C412yes—
14C22×C8×C11—22no—
15C2×C42×C11C2×C411yescharacteristic
16C2×C42×C11C2×C411yescharacteristic
17C2×C42×C11C2×C411yescharacteristic
18C2×C42×C11D411yescharacteristic
19C2×C42×C11D411yescharacteristic
20C2×C42×C11D411yescharacteristic
21C2×C42×C11Q811yescharacteristic
22C22×C11⋊C8—22no—
23C22×C11⋊C8—22no—
24C4⋊(C11⋊C8)—24no—
25#66867—24no—
26#66867—42no—
27#7043—111nomaximal, Sylow
28C22×C4×C11C4211yescharacteristic
29C22×C4×C11C22⋊C411yescharacteristic
30C22×C4×C11C22⋊C411yescharacteristic
31C22×C4×C11C22⋊C411yescharacteristic
32C22×C4×C11C4⋊C411yescharacteristic
33C22×C4×C11C4⋊C411yescharacteristic
34C22×C4×C11C4⋊C411yescharacteristic
35C2×C8×C11—42no—
36C2×C8×C11—42no—
37C2×C8×C11—42no—
38C42×C11—21no—
39C42×C11—21no—
40C42×C11—22no—
41C42×C11—22no—
42C42×C11—22no—
43C42×C11—41no—
44C42×C11—41no—
45C42×C11—41no—
46C2×C11⋊C8—24no—
47C2×C11⋊C8—24no—
48C2×C11⋊C8—42no—
49C2×C11⋊C8—42no—
50C2×C11⋊C8—42no—
51C2×C11⋊C8—42no—
52#1839D1111yescharacteristic
53#1767—111no—
54#1745—111no—
55C23×C11#9511yescharacteristic
56C2×C4×C11—21no—
57C2×C4×C11—21no—
58C2×C4×C11—21no—
59C2×C4×C11—21no—
60C2×C4×C11—21no—
61C2×C4×C11—21no—
62C2×C4×C11—21no—
63C2×C4×C11—21no—
64C2×C4×C11—21no—
65C2×C4×C11—21no—
66C2×C4×C11—21no—
67C2×C4×C11—21no—
68C2×C4×C11—21no—
69C2×C4×C11—21no—
70C2×C4×C11—21no—
71C2×C4×C11—21no—
72C2×C4×C11—21no—
73C2×C4×C11#10011yescharacteristic
74C2×C4×C11#10111yescharacteristic
75C2×C4×C11#10412yes—
76C2×C4×C11#10412yes—
77C2×C4×C11#10812yes—
78C8×C11—82no—
79C11⋊C8—44no—
80C11⋊C8—44no—
81C2×C4⋊C8—221no—
82C2×#97—112no—
83C2×#97—221no—
84C43C2×D1111yescharacteristic
85#336—21no—
86#336—21no—
87#336—112no—
88#336—221no—
89#336—221no—
90#336Dic1112yes—
91C22×C11H(3,ℤ/4)11yescharacteristic
92C22×C11#33911yescharacteristic
93C22×C11#33911yescharacteristic
94C22×C11#34111yescharacteristic
95C22×C11#34311yescharacteristic
96C22×C11#34411yescharacteristic
97C22×C11#34411yescharacteristic
98C4×C11—21no—
99C4×C11—21no—
100C4×C11—22no—
101C4×C11—22no—
102C4×C11—22no—
103C4×C11—41no—
104C4×C11—41no—
105C4×C11—41no—
106C22×C8—22no—
107C22×C8—222no—
108C22×C8—222no—
109C2×C42Dic2211yescharacteristic
110C2×C42C4×D1111yescharacteristic
111C2×C42C4×D1111yescharacteristic
112C2×C42D4411yescharacteristic
113C2×C42C2×Dic1111yescharacteristic
114C2×C42C22⋊D1111yescharacteristic
115C2×C42C22⋊D1111yescharacteristic
116C4⋊C8—224no—
117#97—224no—
118#97—442no—
119C2×C11#128511yescharacteristic
120C2×C11#128711yescharacteristic
121C2×C11#128811yescharacteristic
122C2×C11#129911yescharacteristic
123C2×C11#130011yescharacteristic
124C2×C11#130211yescharacteristic
125C2×C11#130711yescharacteristic
126C22×C4C4×Dic1111yescharacteristic
127C22×C4Dic11⋊C411yescharacteristic
128C22×C4Dic11⋊C411yescharacteristic
129C22×C4C4⋊Dic1111yescharacteristic
130C22×C4(C2×D11)⋊C411yescharacteristic
131C22×C4(C2×D11)⋊C411yescharacteristic
132C22×C4C22⋊Dic1111yescharacteristic
133C2×C8—42no—
134C2×C8—42no—
135C2×C8—42no—
136C2×C8—224no—
137C2×C8—224no—
138C2×C8—442no—
139C2×C8—442no—
140C2×C8—442no—
141C2×C8—442no—
142C42—22no—
143C42—21no—
144C42—21no—
145C42—22no—
146C42—22no—
147C42—41no—
148C42—41no—
149C42—41no—
150C11#704311yescharacteristic, complemented, Sylow
151C23C11⋊#9511yescharacteristic
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—21no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—21no—
162C2×C4—21no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4#6688312yes—
170C2×C4#6688711yescharacteristic
171C2×C4#6688811yescharacteristic
172C2×C4#6688912yes—
173C2×C4#6690112yes—
174C8—82no—
175C8—444no—
176C8—444no—
177C22#1062216911yescharacteristic
178C22#1062217011yescharacteristic
179C22#1062217111yescharacteristic
180C22#1062219011yescharacteristic
181C22#1062219211yescharacteristic
182C22#1062219311yescharacteristic
183C22#1062219411yescharacteristic
184C4—22no—
185C4—22no—
186C4—21no—
187C4—21no—
188C4—22no—
189C4—41no—
190C4—41no—
191C4—41no—
192C2#1306647111yescharacteristic
193C2#1306647811yescharacteristic
194C2#1306648011yescharacteristic
195C2#1306650711yescharacteristic
196C2#1306650811yescharacteristic
197C2#1306651611yescharacteristic
198C2#1306652611yescharacteristic
subgroupG/H
centerC23C11⋊#95
commutatorC22×C4×C11C42
FrattiniC43C2×D11
FittingC11×#1839C2
socle, prime radicalC23×C11#95
cosocleC43×C11C22
hypercenter#1839D11
hypocenterC11#7043
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C43 ◁ #1839

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
150. C11#7043semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#130684692
#130683652
C11×#18392
#704311